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Step2b
Moreover, by assumption, |Aw| defines a birational map and vol(Aw) is bounded from above.
---- 此句出现了“方法”的实例.
---- map 是 “法”, 有界为 “方”.
---- Aw 做成线性系统 |Aw|, 它定义双有理映射.
---- Aw 求体积 vol(Aw), 它有上界.
vol(·) 方
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| · | 法
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评论: Aw 是之前"凭空"变出来的.
---- φ*(-nKx) ~ Aw + Rw. (Step2, 第一句).
---- 上式可看作 “关系方程”, 其中φ*(-nKx) 是已有, 而 Rw 是其固定部分, 而 Aw 是方程的 “解”.
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疑问: 此处的 Aw 跟预配置Th1.6(≤ d) 的 A 有何关系 ?
---- 预配置可能只是用来套用的.
---- 此处 Aw 做 pushdown 得到 A.
---- 这个 A 不是预配置给的, 但会满足预配置的要求.(待考)
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Therefore, by [12, Lemma 3.2], degAwΣw is bounded from above, so by [12, Lemmas 2.4.2(4)], (W, Σw) belongs to a birationally bounded set of pairs depending only on d, eps, n.
---- degAwΣw 有上界; (W, Σw) 属于(双有理)有界族.
---- 这里出现了 度和配对.
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More precisely, if W --> W⁻ is the contraction defined by Aw, then (W⁻, Σw⁻) belongs to a bounded set of couples where Σw⁻ is the pushdown of Σw.
---- 换到 W⁻空间描述.
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评论: -Kx, -nKx, φ*(-nKx), vol(·), |·| 等都可以看作“单词”.
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小结: Step2b(第一段第二节)读写完毕..
符号大全、上下标.|| 常用:↑↓ πΓΔΛΘΩμφΣ∈ ∉ ∪ ∩ ⊆ ⊇ ⊂ ⊃ ≤ ≥ ⌊ ⌋ ⌈ ⌉ ≠ ≡ ⁻⁺⁰ ¹ ² ³ ᵈ ₀ ₁ ₂ ₃ ᵢ .
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第一轮读写链接(按目录顺序)
Abstract 8/4
Introduction
Boundedness of singular Fano varieties (1) 8/5
Boundedness of singular Fano varieties (2) 8/6
Boundedness of singular Fano varieties (3) 8/7
Boundedness of singular Fano varieties (4) 8/8
Boundedness of singular Fano varieties (5) 8/9
Boundedness of singular Fano varieties (6) 8/9
Jordan property of Cremona groups 8/10
Lc thresholds of lR-linear systems 8/11
Lc thresholds of anti-log canonical systems of Fano pairs (1) 8/12
Lc thresholds of anti-log canonical systems of Fano pairs (2) 8/13
Lc thresholds of R-linear systems with bounded degree 8/14
Complements near a divisor 8/15
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.Proposition 5.2 11/9
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Proposition 5.5. 11/5
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